Question

The relation R is defined on the set of natural numbers as $\left\{(a,b):a=2b\right\}$. Then $R^{-1}$ is given by

• A. $\left\{(2,1),(4,2),(6,3),\dots \right\}$
• B. $\left\{(1,2),(2,4),(3,6),\dots \right\}$
• C. $R^{-1}$ is not defined
• D. None of the above

Answer 1

The correct option is B

$\left\{(1,2),(2,4),(3,6),\dots \right\}$

Explanation for he correct option:

Write the elements of the given relation.

Given, $a=2b$.

So,

When $b=1$, then $a=2$

When $b=2$, then $a=4$

When $b=3$, then $a=6$

When $b=4$, then $a=8$

Thus the relation R can be written as:

$R=\left\{(2,1),(4,2),(6,3),\dots .\right\}$

For $R^{-1}$, we need to interchange the position of $a$ and $b$.

So, the relation $R^{-1}$ can be written as:

$R^{-1}=\left\{(1,2),(2,4),(3,6),\dots \right\}$

Hence, option $B$ is the correct answer.